Entanglement Spreading and Oscillation

TL;DR

This paper investigates the dynamics of quantum entanglement in 1+1 dimensional free scalar theories under smooth global quenches, revealing how entanglement entropy evolves, oscillates, and relates to critical points and quench rates.

Contribution

It provides an exactly solvable model for entanglement dynamics during smooth quenches crossing or approaching critical points, highlighting oscillatory behavior and scale-dependent proportionalities.

Findings

Entanglement entropy scales linearly with time and subsystem size in certain regimes.

Entropy oscillations are linked to coherence between wave modes and zero-mode periodicity.

Different scales govern entanglement growth in fast and slow quench limits.

Abstract

We study dynamics of quantum entanglement in smooth global quenches with a finite rate, by computing the time evolution of entanglement entropy in 1 + 1 dimensional free scalar theory with time-dependent masses which start from a nonzero value at early time and either crosses or approaches zero. The time-dependence is chosen so that the quantum dynamics is exactly solvable. If the quenches asymptotically approach a critical point at late time, the early-time and late-time entropies are proportional to the time and subsystem size respectively. Their proportionality coefficients are determined by scales: in a fast limit, an initial correlation length; in a slow limit, an effective scale defined when adiabaticity breaks down. If the quenches cross a critical point, the time evolution of entropy is characterized by the scales: the initial correlation length in the fast limit and the effective correlation length in the slow limit. The entropy oscillates, and the entanglement oscillation comes from a coherence between right-moving and left-moving waves if we measure the entropy after time characterized by the quench rate. The periodicity of the late-time oscillation is consistent with the periodicity of the oscillation of zero modes which are zero-momentum spectra of two point functions of a fundamental field and its conjugate momentum.